Disclaimer. We're unschoolers. I believe strongly that curiosity is as innate to being human as swimming is to fish and flying to birds. Children want to learn about their world and become functioning adults - unless they have been taught by schools that learning can only happen in ways that are boring and that they aren't good at. Check out The Heart of Unschooling, Q&A to learn more and to find out if it really prepares kids for college and real life.
That said, I fully support that each family must find what works for them and few will actually unschool.
When folks first think of homeschooling they think of replicating school at home. Ultimately, very few homeschoolers stay in this place. There's a very wide spectrum from school-at-home on the one hand to unschooling on the other hand. Most homeschoolers end up somewhere in the middle, finding out that reading/writing/worksheets/textbooks are not usually the most ideal way for their child to learn. In fact, research shows that children learn best when in relationship with others with multiple senses engaged in an activity that interests them. Think about when you want to learn something... I bet you seldom order a textbook, fill out worksheets, and take a test. ;) You probably Google, read a *REAL* book, talk to people who know more than you, and do some hand's on experimenting. You probably talk to people about what you're learning because you're excited about it and discuss it with other folks interested in the same topic. This is the real life way that knowledge gets reinforced and built upon.
Most folks starting off want a curriculum at least for reference, but keeping an open mind to how learning can work outside of that curriculum is important too. Ask around on homeschool pages and you'll get 101 different recommendations for curriculums. Go ahead and choose one. Just hold it loosely. Use the wording I recommend in my How to Homeschool in NYS post so you can change things up if you find something else that works better. And be willing to follow your child's lead when they go down a rabbit hole and want to veer off the curriculum. That's the joy of learning happening right there! Celebrate it!
See my post on some of our favorite learning resources along with our homeschool/unschool posts over the years for ideas of how subjects can be covered via real life.
Here are a few ways learning has happened naturally, over the years, in our home.... in note form for each subject.
Math - we skip counted, counted by 5's and 10's and 100's in the car. We made up stupid/nonsense/gross poems for the times tables. We watched the zany math antics dot com and the British Maths Mansion on YouTube. We played the Dragon Box app and the Prodigy math game. We read library story books on math topics such as Multiplying Menace. This got us through middle school math. For high school, my daughter meets weekly with a tutor. I don't do high school math!
English - we read 1001 library books; we read books we own; we listened to audio books; usually I did the reading since my daughter has dyslexia and never loved to read. Now, at age 15, she reads just fine, but still prefers an audio book. We didn't label her as "learning disabled" just because her learning style was different from the school-norm. There was no need to label her at home. Vocabulary was learned through real life and reading. Grammar was learned through me gently correcting thing she said with explanations of why one way was correct - plus MadLibs. Everyone should play MadLibs with their kids and allow them to put in as many potty words as they want! ;) Your kid will be an expert on verbs and nouns and adjectives and adverbs in no time and you'll all be laughing hilariously! For writing, see my post on How Unschoolers Learn to Write.
Social - we watched Little House and talked about what life was like in those times. We read Native American stories and stories about holidays in other cultures. We read Magic Treehouse and talked about fact vs fiction. Historical fiction - whether through books or films - has always been a HUGE part of learning history here. It's by far more engaging than the dry facts and dates in a textbook, and of course you want to look up a few facts to see what's real vs not real. Liberty Kids is great for little ones (free on YouTube). Howard Zinn's Young People's History of the US book, Crash Course videos (US History, World History, European History), and the Seeds of American Trilogy (books) are all engaging for older kids. We did use Story of the World (SOTW) for World History the first time around, but I have a lot of reservations about it, key being that it centers around "now so and so was the richest and most powerful man in the world". See my Ancient History post on how we used SOTW for discussion of who gets to write history and how we supplemented it.
Science - have you ever wondered why kids learn about cells and molecules but can't tell you about the plants and animals in their neighborhood? We started with several years of natural science, focusing on feeding and identifying birds, reading stories about the lives of animals around us, learning about the seasons, learning about the migration of a hummingbird from a fictional story, going to wilderness school, foraging for wild edibles, growing a garden, and so on. Books I read to her featured heavily here - enchanting fictional stories that taught real life science about the world around us. There are so very many wonderful books! From there, Helena branched into topics like biology, regenerative ecology, and now astronomy.